trees. faster than linear data structures more natural fit for some kinds of data examples? why a...
TRANSCRIPT
Trees
• Faster than linear data structures
• More natural fit for some kinds of data• Examples?
Why a tree?
Example Tree
root
ActivitiesTeaching Research
Sami’s Home Page
Papers PresentationsCS211CS101
Terminology
• Root• Parent • Child• Sibling• External node• Internal node• Subtree• Ancestor• Descendant
Example Tree
root
ActivitiesTeaching Research
Sami’s Home Page
Papers PresentationsCS211CS101
Root?Parent – papers, activities Children – cs101, research Sibling - teaching
External nodesInternal nodesSubtree – left subtree of research?Ancestor – papers ancestor of activities?Descendant – papers descendant of home?
Ordered Trees
• Linear relationship between child nodes
• Binary tree – max two children per node – Left child, right child
Davidson Truman
Rollins
Taft ZunigaRalsonBrown
root
Another Ordered Binary Tree
Ralson
Truman
Brown
Taft Zuniga
RollinsDavidson
root
Tree Traversal
• Pre-order traversal– Visit node, traverse left subtree, traverse right
subtree
• Post-order traversal– Traverse left subtree, traverse right subtree,
visit node
Example
• Pre-order
• Post-order
Davidson Truman
Rollins
Taft ZunigaRalsonBrown
root
Example
• Pre – Rollins, Davidson, Brown, Ralson, Truman, Taft, Zuniga
• Post – Brown, Ralson, Davidson, Taft, Zuniga, Truman, Rollins
Do Trimmer
Rollins
Tilkidjieva YuciusReardonBendersky
root
Another Example
Ralson
Truman
Brown
Taft Zuniga
RollinsDavidson
root
• Pre – Brown, Truman, Taft, Ralson, Davidson, Rollins, Zuniga
• Post – Davidson, Rollins, Ralson, Taft, Zuniga, Truman, Brown
In-order Traversal
• Traverse left subtree, visit node, traverse right subtree– Brown, Davidson, Ralson, Rollins, Taft,
Truman, Zuniga
Davidson Truman
Rollins
Taft ZunigaRalsonBrown
root
Another Example
Ralson
Truman
Brown
Taft Zuniga
RollinsDavidson
root
• In-order – Brown, Davidson, Ralson, Rollins, Taft, Truman, Zuniga
Implementation – TreeNode
• Data members?
• Functions?
Name = Rollins
Implementation – Tree
• Data Members
• Functions– Pre/post/in-order print
Smith
Rollinsroot
Brown
Implementation – Pre-order
void preOrderPrint(TreeNode* curnode) {o.print();if(curnode->getLeftChild() != NULL)
preOrderPrint(curnode->getLeftChild());if(curnode->getRightChild() != NULL)
preOrderPrint(curnode->getRightChild());
}
Tree* t = …; t->preOrderPrint(t->getRoot());
BSTs
• Elements in left subtree nodes are before (are less than) element in current node
• Element in current node is before (less than) elements in right subtree
find Operation
• Algorithm for finding element in BST
Ralson
Truman
Brown
Taft Zuniga
RollinsDavidson
root
find Algorithm
if current node is null
return not found
else if target is in current node
return found
else if target is before current node
return find(left child)
else
return find(right child)
find Complexity
• Worst case
• Best case
• Average case
insert Operation
• Algorithm for inserting element in BST
Ralson
Truman
Brown
Taft Zuniga
RollinsDavidson
root
insert Algorithm
if new_elt is before current and current left child is null
insert as left child
else if new_elt is after current and current right child is null
insert as right child
else if new_elt is before current
insert in left subtree
else
insert in right subtree
remove Operation
• Algorithm for removing element in BST
Ralson
Truman
Brown
Taft Zuniga
RollinsDavidson
root
remove Algorithm
elt = find node to remove
if elt left subtree is null
replace elt with right subtree
else if elt right subtree is null
replace with left subtree
else
find successor of elt
(go right once and then left until you hit null)
replace elt with successor
call remove on successor